Natural materials, as well as many engineered materials, are heterogeneous, whereby the physical properties of such materials spatially vary, and occur with randomness. For example, polymer matrices, metal matrix composites, cementitous materials, and natural materials (e.g. wood, geo-materials, and bones) exhibit heterogeneity at various scales. In other words, spatial variation of material properties is inherent to heterogeneous materials, and in some cases may be the result of physical damage when such materials are subjected to various loadings and forces. However, reliable structural design utilizing heterogeneous materials requires the rigorous consideration of various spatial randomness parameters (i.e. stochastic parameters) that characterize the spatial variation of properties of such materials. For example, such stochastic parameters may include spatial mean, spatial variance and correlation length.
To meet this growing need to characterize the stochastic parameters of heterogeneous materials, there has been a growing need for statistical characterization tools. Unfortunately, adequate tools for identifying key stochastic parameters of materials are unavailable, and as a result, engineers and researchers have been forced to make generalized assumptions regarding the qualitative and quantitative information of such stochastic parameters during virtual model simulations that utilize heterogeneous materials. However, probabilistic simulation results using such assumptions of the random properties of heterogeneous materials lack accuracy and reliability that is required to achieve acceptable results.
Alternatively, the characterization of the uncertainties or randomness of heterogeneous materials could be obtained from direct measurement of the material in the field. However, the ability to obtain direct measurements of the spatially correlated random properties of materials is very limited, even at the micro-scale, due to the required use of expensive measurement techniques, the lack of well-defined procedures, and the difficulties encountered in handling the large amount of data that is generated.
Therefore, there is a need for an indirect method of identifying stochastic parameters of heterogeneous materials, which include, but is not limited to the statistical parameters of: spatial mean, spatial variance, and correlation length of the spatially varying properties of heterogeneous materials. In addition, there is a need for a method of identifying stochastic parameters of a heterogeneous material that is used to reconstruct spatial distributions of random properties of a material with reference to experimental material test data. Additionally, there is a need for a method of reconstructing the spatial distribution of a specific random field in which one realization of the random filed that holds stochastic characteristics is identified, thus allowing diagnosis of material states under services and operations. Furthermore, there is a need for a systematic method of identifying probabilistic information of stochastic parameters of heterogeneous materials, which can be used to generate a statistically equivalent sample material model for use in developing probabilistic models or conducting reliability-based design of structures using such heterogeneous materials. In addition, there is a need for a method of identifying the stochastic parameters of a material using a self-optimizing inverse computation technique (Self-OPTIM).